Constructing small sample spaces satisfying given constraints

Abstract. The subject of this paper is nding small sample spaces for joint distributions of n discrete random variables. Such distributions are often only required to obey a certain limited set of constraints of the form Pr(E) = . We show that the problem of deciding whether there exists any distribution satisfying a given set of constraints is NP-hard. However, if the constraints are consistent, then there exists a distribution satisfying them which is supported by a \small" sample space (one whose cardinality is equal to the number of constraints). For the important case of independence constraints, where the constraints have a certain form and are consistent with a joint distribution of n independent random variables, a small sample space can be constructed in polynomial time. This last result is also useful for de-randomizing algorithms. We demonstrate this technique by an application to the problem of nding large independent sets in sparse hypergraphs. Department of Computer...

• Type: Conference
• Year: 1993
• Where: STOC
• Authors: Daphne Koller, Nimrod Megiddo
• Keywords: Algorithms, IBM Almaden Research Center, Sample Space, Small Sample Space, STOC 1993